The Adagio, BWV 1001, not only opens the G-minor sonata, but it also opens the whole collection of Sonatas and Partitas.
Just as the opening chord is a quintessential violin chord, one might also say that the structure of this entire movement is quintessential to violin technique.
Built in three sections, the last section mirrors the first, but transposed up a fifth. On the violin, when transposing up a fifth, one can just repeat the exact same thing one string higher.
However, with Bach, things never get repeated exactly; they are developed and varied and, as this video shows, there are a few notable places where he deviates from his plan.
Looking at how these sections differed was a very important part of our work while arranging the Sonatas and Partitas, and, in the same vein, understanding these issues will help all musicians, whether they are arrangers, performers, or listeners.